Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we first propose a new classification of non-rigid registratio- n algorithms into three main categories: in one hand, the geometric algorithms- , and in the other hand, intensity based methods that we split here into standard intensity-based (SIB) and pair-and-smooth (P&S) algorithms. We then focus on the subset of SIB and P&S algorithms that are competitive, i.e. that use a regularization energy which is minimized together with the intensity similarity energy. In SIB algorithms, these two energies are combined in a weighted sum, and thus the trade-off between them is direct. P&S algorithms alternates their respective minimization, leading to the characteristic two steps: pairing of points, and smoothing. We theoretically compare the behavior of SIB and P&S algorithms, and more precisely, we explain why in practice the smoothness of the transforms estimated by SIB algorithms is non-uniform, thus difficult to control, while P&S algorithms estimate a motion that is more uniformly smooth. We give an example illustrating this behavior. Very few P&S algorithms minimize a global energy. We therefore propose a new image registration energy whose minimization leads to a \PAS algorithm. This energy is general, and can use any existing similarity or regularization energy. Its behavior is also compared to the previous SIB and \PAS algorithms. This new energy allows uniformly smooth solutions, as for our previous P&S algorithm, while preventing registration of non-informative, noisy areas, as for SIB algorithms

Fast Non Rigid Matching by Gradient Descent: Study and Improvements of the "Demons" Algorithm

Most iconic methods for rigid matching consist in finding and minimizing a registration criterion specifically chosen to solve a given problem. For non-rigid matching, attention has rather focussed on the type of smoothing or physical model of deformation to be used. In this report, we propose to place the non-rigid matching problem into a minimization framework. We have developped our theoretical idea in the case of the least squares criterion, corresponding to the assumption that the intensities of points do not change over time, and we have implemented a first order gradient descent which, along with a multiresolution approach, minimizes this criterion- . We also prove that the «demons» algorithm, thought of until now as an as hoc matching technique, can be seen as an approximation of a second order gradient descent on this criterion. Analysis of the mechanisms of this gradient descent incites us to introduce two different weightings into the filters used to smooth the solution, which we called an a priori weighting improves the solution found for the minimization problem, which is shown by comparing results in a distance-roughness space, while the a posteriori weighting helps tackle the appearance or disappearance of matter and occlusions, both sensitive issues for non-rigid iconic methods

Recalage non rigide d'images médicales volumiques : contributions aux approches iconiques et géométriques

Non-rigid image registration is a classical problem in computer vision that consists in deforming one image so that it follows the geometry of another image. Registration techniques are very numerous, and are generally classified according to the kind of features they use in the images to deform them. On one hand, intensity-based algorithms use the intensity of the images. On the other hand, geometric algorithms use geometric features segmented from the images, such as object boundaries. In this thesis, we first show that this classification is not fine enough to explain some fundamental differences between some registration algorithms. We propose to part the intensity-based algorithms in two classes : we distinguish between the standard intensity based (SIB) algorithms, and the intensity feature based (IFB) algorithms. We introduce a general registration energy for iconic feature registration; then, we develop particular instances of this energy with special properties according to the application : additional geometric constraints obtained from a segmentatio- n, non uniform bias invariance, vectorial regularization with cross-effects between coordinates, invariance by exchange of the images to be registered. We give applications of our algorithm in brain tracking in volumetric ultrasound image sequences, in inter-subject brain registration using magnetic resonance imaging, and in shape-and-intensity interpolation.Le recalage non rigide d'images est un problème classique en vision par ordinateur qui revient à déformer une image afin qu'elle ressemble à une autre. Les techniques existantes, très nombreuses, sont généralement répertoriées selon l'information utilisée pour le recalage. D'un côté les algorithmes iconiques utilisent l'intensité des images. De l'autre, les algorithmes géométiques utilisent des amers géométriques extraits des images, comme les bords d'un objet. Dans cette thèse, nous montrons d'abord que cette classification n'est pas assez fine pour expliquer certaines différences fondamentales dans le comportement de certains algorithmes. Nous proposons de ce fait de diviser la classe des algorithmes iconiques en deux : nous distinguons d'une part les algorithmes iconiques standard, et d'autre part les algorithmes de recalage d'amers iconiques. Nous introduisons une énergie générale de recalage d'amers iconiques, puis nous développons des instances particulières de cette énergie ayant des propriétés spéciales selon l'application visée : ajout de contraintes géométriques supplémentaires, invariance au biais non uniforme, régularisation vectorielle avec des effets croisés, invariance par échange des images. Nous montrons des applications de nos algorithmes en suivi du mouvement dans des séquences échographiques tridimensionnelles, en relage intersujet de cerveaux, et en interpolation de formes et d'intensités

How to trade off between Regularization and Image Similarity in Non-rigid Registration?

International audienceno abstrac

Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we #rst propose a new classi#cation of non-rigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensity-based #SIB# and pairand -smooth #P&S# algorithms

Isotropic energies, filters and splines for vectorial regularization

International audienceno abstrac

Symmetrization of the Non-Rigid Registration Probem using Inversion-Invariant Energies: Application to Multiple Sclerosis

International audienceno abstrac

Regularization in Image Non-Rigid Registration: I. Trade-off between Smoothness and Intensity Similarity

In this report, we first propose a new classification of non-rigid registration algorithms into three main categories: in one hand, the geometric algorithms, and in the other hand, intensity based methods that we split here into standard intensity-based (SIB) and pair-and-smooth (P&S) algorithms. We then focus on the subset of SIB and P&S..